1. Field of the Invention
The present invention is directed to a method for the fast acquisition of a magnetic resonance image, wherein magnetic resonance signals from an imaging region are acted on by magnetic gradient fields that define a spatial frequency space so that the spatial frequency space is occupied with magnetic resonance signals having trajectories that are radially directed and proceed through a projection center.
2. Description of the Prior Art
A method of the above type is described in the book by Heinz Morneburg, xe2x80x9cBildgebende Systems fxc3xcr die medizinische Diagnostik,xe2x80x9d Publicis MCD Verlag, 3rd edition, 1995, pages 176-183.
The localization of the magnetic resonance signals from a subject to be imaged that is necessary for the imaging ensues by superimposition of a uniform magnetic basic field with a magnetic field gradient. When a two-dimensional examination subject is assumed wherein the magnetization aligned by the basic magnetic field was tilted out of the equilibrium position by means of a radio-frequency pulse, then the Larmor frequency is constant in stripes perpendicular to the gradient direction when a gradient field is applied. In other words, the signal amplitude of the magnetic resonance signal as a function of the frequency respectively corresponds to the sum of all spins in this stripe, i.e. represents the projection of the transverse magnetization onto the field gradient. The signal that is detected by the measurement, however, is the time signal that is registered by means of suitable antennas. During further processing, an alternating voltage similar to the Larmor frequency is admixed with the received magnetic resonance signal, so that the signal of the difference frequency (phase-sensitive rectification) directly indicates the magnetic moment of the precessing nuclear magnetization. With the introduction of a xe2x80x9cnormalized timexe2x80x9d or spatial frequency k established by k=xcex3∫Gxc2x7dt, where xcex3 is the gyromagnetic ratio, G is the magnetic field gradient and t is the time during which the magnetic field gradient is superimposed on the magnetic basic field, the measured signal and the projection prove to be a Fourier transform pair. A set of magnetic resonance signals that are generated in successively stepped gradients is, accordingly, the two-dimensional Fourier transform of the magnetization. The Fourier space, spatial frequency domain or k-space inverse to the spatial or image domain wherein the test subject is located is thus scanned with a raster of polar coordinates. The graphic presentation of the magnetization, however, ensues in Cartesian coordinates. The magnetic resonance image then can be generated with two different methods. In the first method, the received magnetic resonance signals are re-interpolated onto a Cartesian grid and are subjected to a two-dimensional Fourier transformation. In a second method, the received magnetic resonance signals are subjected to a one-dimensional Fourier transformation, as a result of which projections are calculated and the image is then reconstructed by means of a filtered back-projection.
For imaging three-dimensional subjects, the above considerations for two-dimensional imaging are expanded by one dimension. When it is assumed in the two-dimensional case that N projections are registered, N2 projections must be registered in the three-dimensional case given the same resolution in the third dimension. If it is desired to avoid the lengthening on the measurement time resulting therefrom and to graphically present only one slice, this slice is cut (defined) from the spatial test subject by means of xe2x80x9cselective excitationxe2x80x9d, this then being two-dimensionally measured.
The radial scanning of the spatial frequency domain mentioned above is of interest for magnetic resonance imaging because it enables shorter repetition times in the image sequence compared to the occupation of the spatial frequency domain in Cartesian coordinates and is less susceptible to motion artifacts. The shortening of the repetition time arises from the absence of the additional phase coding steps required given Cartesian scanning directions.
Various other methods are known in general for reducing the exposure times in magnetic resonance imaging that are based on parallel and simultaneous data pickup of the magnetic resonance signals with a number of antennas of an antenna array (PPA, or partial parallel acquisition, methods). The number of lines in the spatial frequency domain to be acquired thus can be reduced in conformity with the number of antennas utilized.
One such method is described in the article by Daniel K. Sodicksen, Warren J. Manning, xe2x80x9cSimultaneous Acquisition of Spatial Harmonics (SMASH): Fast Imaging with Radiofrequency Coil Arraysxe2x80x9d, which appeared in Magnetic Resonance in Medicine, Volume 38, 1997, pages 591 through 603. The location coding or conditioning of the spins therein ensues with phase coding gradients and frequency coding gradients. The spatial frequency space is thus scanned on a Cartesian grid. The magnetic resonance signals, however, are conditioned such that scanning in phase coding direction is only incomplete. The excited magnetic resonance signals, however, are simultaneously received with an antenna array composed of a number of antennas. Because the individual k-space rows are multiplied by weighting factors that are determined from the sensitivity profiles of the antennas (which are assumed to be known), the missing k-space rows can be synthesized, so that k-space is completed in the phase coding direction. A gain in measuring time thus is achieved that corresponds to the phase coding steps that are saved.
The article by Klaas P. Pruessmann, Markus Weiger, Markus B. Scheidecker and Peter Boesiger, xe2x80x9cSense: Sensitivity Encoding for Fast MRIxe2x80x9d, which appeared in Magnetic Resonance in Medicine, Volume 42, 1999, pages 952 through 962, describes a PPA method wherein the signals received from the individual antennas, that are incomplete in the phase coding direction, are first subjected to a Fourier transformation. The partial images that are generated in this way, however, exhibit convolutions in the phase coding direction due to the under-scanning. The individual images are then superimposed form a convolution-free overall image using the known sensitivity profiles.
The article by Mark A. Griswold, Peter M. Jakob, Mathias Nittka, James W. Goldfarb and Axel Haase, xe2x80x9cPartially Parallel Imaging With Localized Sensitivities (PILS)xe2x80x9d, which appeared in Magnetic Resonance in Medicine, Volume 44, 2000, pages 602-609, describes a further PPA method. It is thereby assumed that the individual antennas in the antenna array have only a limited sensitivity profile. It is then adequate for the antennas to be characterized by only two parameters: the position of the center of the sensitivity zone of the corresponding antenna in the overall field of view and the width of the sensitivity zone around this center.
An object of the present invention is based on the object of specifying a method for fast acquisition of a magnetic resonance image wherein the measuring time that has already been inherently shortened is reduced further given radial scanning of the spatial frequency space.
This object is achieved in a method in accordance with the invention wherein the imaging zone is subdivided into sub-regions; with an antenna of an antenna array allocated to each sub-region. Each antenna has a known position relative to the projection center; and the antennas simultaneously receive the magnetic resonance signals and respectively form reception signals from the received magnetic resonance signals according to their sensitivity. The number of radially directed trajectories is of such a size so that only the sub-zonesxe2x80x94regardless of their spatial position in the imaging zonexe2x80x94can be unambiguously reconstructed; from the respectively received signals. The reception signals, taking the positions of the individual receiving antenna into consideration, are transformed in a transformation step to form a magnetic resonance image of the entire imaging zone. The sampling increment along the trajectories for the signals of the individual antennas in k-space is always selected so small, i.e. the number of sampling steps is made so large, that a circle is selected having a diameter that is at least of such a size that the projections of the subject to be imaged fit therein, i.e. it can be presented without fold-overs or clipping. Below, this circle is called the overall image field. The reduction of the measurement time is achieved becausexe2x80x94given the same resolutionxe2x80x94fewer trajectories in k-space are required due to the simultaneous reception of magnetic resonance signals with a number of antennas from sub-zones that are smaller than the overall imaging zone, compared to the situation where the entire imaging zone is covered with a single antenna. Due to the smaller sub-zones compared to the overall imaging zone, each antenna of the antenna array also receives less noise, so that a better signal-to-noise ratio also is achieved with reference to the measurement time.
In on embodiment, respective projections are formed in the transformation step by a Fourier transformation from the reception signal of the antennas, whose number of angular steps, of course, is reduced in comparison to the number of angular steps that would be required for imaging the overall zone with one coil. The respective projections are back-projected into the imaging zone to form partial images after a filtering. Due to the reduced number of projection steps, each partial image is surrounded by ray-shaped reconstruction artifacts that can be cut off (suppressed) before superimposition of the partial images without loss of information when the position of the individual antennas is known. This is an important calculating step and is the reason why it is advantageous to first reconstruct individual images that are later superimposed. If the signals of the individual coils were not superimposed until they are in k-space and the overall image were then reconstructed in one calculating step, the sampling artifacts that occur due to the reduced number of projection steps could not be removed without further difficulty.
In another embodiment, the reception signals of the individual antennas established on the radial projectories in the spatial frequency domain are transformed in the transformation step onto a rectangular grid, and the partial images allocated to the antennas are reconstructed with a two-dimensional Fourier transformation from the reception signals transformed onto the rectangular grid. It must likewise be taken into consideration that the partial images are surrounded by over-convolution artifacts that must be removed before the superimposition to form the magnetic resonance image.
In another embodiment, the projections obtained by means of the Fourier transformation of the signal values are shifted from the position of the antenna into the projection center before the filtered back-projection, i.e. the origin of the gradient directions. The partial image reconstruction then need not ensue in the overall image field but instead be made in a smaller image field, and the clipping of over-convolution artifacts can be omitted. As a result, the reconstruction time can be shortened. For formatting the overall image, the partial images are again shifted back to the position of the antenna and superimposed.
In another embodiment, the reception signals of the antennas are reinterpolated onto a rectangular grid and are then multiplied by a phase factor derived from the distance of the respective antenna from the projection center. The partial images obtained after two-dimensional Fourier transformation are shifted back again corresponding to the positions of the antennas and are superimposed to form the overall image. A shift is utilized is a shift in the locus or image domain in the Fourier space corresponding to an additional phase in the spatial frequency domain.
In a further embodiment uses a technique similar to the SMASH method, wherein a completely occupied spatial frequency domain of the imaging zone is generated from the reception signals and the sensitivity profiles of the antennas with linear combinations in the transformation step, and in that the magnetic resonance image is reconstructed from the completely occupied spatial frequency domain. The reconstruction to form the overall image ensues by calculating projections by Fourier transformation from the signals that are back-projected filtered, or the signals are re-interpolated onto a rectangular grid and the overall image is acquired by a two-dimensional Fourier transformation. The weighting factors for the linear combinations are selected such that azimuthally harmonically varying functions are built up from the known sensitivity profiles.
In another version of the above-described reconstructions, the partial images are superimposed in a weighted manner. The weighting factors can be selected to achieve a particular result. For example, the weighting factors can be selected so that the variation of the image signal arising due to different sensitivities of the individual coils is compensated, or by weighting the partial images dependent on their own signal content before their superimposition. Using the latter technique, a quality improvement of the magnetic resonance image is achieved because the useful signals with high amplitude are more highly weighted in comparison to noise signals with low amplitude in the superimposition.
In another embodiment, an arbitrarily shaped imaging zone is simulated by round sub-zones in order to thus be able to utilize the advantageous of radial scanning.
The sub-zones then can partially overlap in a version of this embodiment.
Fundamentally, an approximately spherical subject also can be radially scanned in k-space with a coil array and measurement time for the acquisition of a 3D image can be saved by division into partial measuring fields. For the acquisition of individual images, however, it is more beneficial to select a slice from the imaging zone by means of a magnetic gradient field during the RF excitation.